Simplify the following expression: $r = \dfrac{y^2 + 9y + 20}{y + 5} $
Solution: First factor the polynomial in the numerator. $ y^2 + 9y + 20 = (y + 5)(y + 4) $ So we can rewrite the expression as: $r = \dfrac{(y + 5)(y + 4)}{y + 5} $ We can divide the numerator and denominator by $(y + 5)$ on condition that $y \neq -5$ Therefore $r = y + 4; y \neq -5$